Question

use synthetic substitution to evaluate the given value and determine the remainder. f (x) = -4x⁴ + 9x³ + 8x² + 9x - 13 at x = 3

Explanation:

Step1: Set up synthetic division

The coefficients of \( f(x)=-4x^{4}+9x^{3}+8x^{2}+9x - 13 \) are \(-4, 9, 8, 9, -13\), and we use \( x = 3 \) for synthetic substitution.

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Step2: Interpret the result

In synthetic substitution, the last number in the bottom row is the remainder (and also the value of \( f(3) \)).

Answer:

The remainder when \( f(x)=-4x^{4}+9x^{3}+8x^{2}+9x - 13 \) is evaluated at \( x = 3 \) using synthetic substitution is \( 5 \).